Holographic representation of local bulk operators

The Lorentzian AdS/CFT correspondence implies a map between local operators in supergravity and non-local operators in the CFT. By explicit computation we construct CFT operators which are dual to local bulk fields in the semiclassical limit. The computation is done for general dimension in global, Poincare and Rindler coordinates. We find that the CFT operators can be taken to have compact support in a region of the complexified boundary whose size is set by the bulk radial position. We show that at finite N the number of independent commuting operators localized within a bulk volume saturates the holographic bound.Comment: 36 pages, LaTeX, 4 eps figure

A Comment on Zero-brane Quantum Mechanics

We consider low energy, non-relativistic scattering of two Dirichlet zero-branes as an exercise in quantum mechanics. For weak string coupling and sufficiently small velocity, the dynamics is governed by an effective U(2) gauge theory in 0+1 dimensions. At low energies, D-brane scattering can reliably probe distances much shorter than the string scale. The only length scale in the quantum mechanics problem is the eleven dimensional Planck length. This provides evidence for the role of scales shorter than the string length in the weakly coupled dynamics of type IIA strings.Comment: 9 pages, harvmac, improved treatment of 2+1 proble

Constructing local bulk observables in interacting AdS/CFT

Local operators in the bulk of AdS can be represented as smeared operators in the dual CFT. We show how to construct these bulk observables by requiring that the bulk operators commute at spacelike separation. This extends our previous work by taking interactions into account. Large-N factorization plays a key role in the construction. We show diagrammatically how this procedure is related to bulk Feynman diagrams.Comment: 41 pages, LaTeX. v2: reference correcte

Non-Local Effects of Multi-Trace Deformations in the AdS/CFT Correspondence

The AdS/CFT correspondence relates deformations of the CFT by "multi-trace operators" to "non-local string theories". The deformed theories seem to have non-local interactions in the compact directions of space-time; in the gravity approximation the deformed theories involve modified boundary conditions on the fields which are explicitly non-local in the compact directions. In this note we exhibit a particular non-local property of the resulting space-time theory. We show that in the usual backgrounds appearing in the AdS/CFT correspondence, the commutator of two bulk scalar fields at points with a large enough distance between them in the compact directions and a small enough time-like distance between them in AdS vanishes, but this is not always true in the deformed theories. We discuss how this is consistent with causality.Comment: 24 pages, 6 figures, 2 appendices. v2: added reference

An Immunochemical Study of the Combining Sites of the Second Lectin Isolated from \u3ci\u3eBandeiraea simplicifolia\u3c/i\u3e (BS II)

Two lectins with different binding specificities have been isolated from extracts of seeds of Bandeiraea simplicifolia. The first, Bandeiraea lectin I [11] was specific for terminal non-reducing αDGalactosyl residues. It reacted with B substances from human ovarian cysts and with several galactomannans to form precipitin lines in agar gels. Polysaccharides with terminal αDGalactosyl residues, such as larch galactan, did not react. The lectin agglutinated B erythrocytes strongly but also reacted to a lower titre with A1 and very weakly with A2 erythrocytes [15, 28] indicating that terminal non-reducing αDGalNAc [24] can be accommodated in the-site to some extent. Recently, it was shown that B. simplicifolia lectin I (BS I) consists of five isolectins each of which is a tetrameric glycoprotein composed of A and B subunits; the A subunits are specific for αDGalNAc, the B subunits for αDGal [30]. The second lectin, Bandeiraea lectin II (BS II), isolated by affinity chromatography on chitin [13], is a glycoprotein (molecular weight 113,000) of four subunits of molecular weight 30,000. It does not agglutinate A, B or O erythrocytes. Quantitative precipitin assays showed it to react better with BSA conjugated to p-azophenyl αDGalNAc than with the β compound. In inhibition studies, the unusual observation was made that N,N’-diacetylchitobiose (DGlcNAcβ1 → 4DGlcNAc) and pNO2 phenyl αDGalNAc were highly active; methyl αDGalNAc was only one half as active but was eight times more active than methyl βDGlcNAc